Geometry: Right Circular Hollow Cylinder

 Right Circular Hollow Cylinder Let R and r be the external and internal radii of a hollow cylinder of height h. Then, (i) Area of each end = (R2 -r2) (ii) Curved surface area of hollow cylinder = External surface area + Internal surface area = 2Rh+2rh = 2h(R + r) (iii) Total surface area = Curved surface area + 2 (Area of base ring) = 2Rh + 2rh + 2( R2 - r2) = 2Rh(R + r) + 2(R + r)(R - r) = 2(R + r) (R + h - r) (iv)Volume of material = External volume - Internal volume = (R2 - r2)h
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 Example: Find the volume of cylinder with inner radius 7 cm, outer radius 10 cm and height 18 cm. Solution: Volume = (R2 - r2 )h =3.142 x (102 - 72 ) x 18 cm3 =2884.356 cm3

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